2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include "isl_equalities.h"
17 #include <isl_space_private.h>
18 #include <isl_mat_private.h>
20 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
22 isl_int *t = bmap->eq[a];
23 bmap->eq[a] = bmap->eq[b];
27 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
30 isl_int *t = bmap->ineq[a];
31 bmap->ineq[a] = bmap->ineq[b];
36 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
38 isl_seq_cpy(c, c + n, rem);
39 isl_seq_clr(c + rem, n);
42 /* Drop n dimensions starting at first.
44 * In principle, this frees up some extra variables as the number
45 * of columns remains constant, but we would have to extend
46 * the div array too as the number of rows in this array is assumed
47 * to be equal to extra.
49 struct isl_basic_set *isl_basic_set_drop_dims(
50 struct isl_basic_set *bset, unsigned first, unsigned n)
57 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
59 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
62 bset = isl_basic_set_cow(bset);
66 for (i = 0; i < bset->n_eq; ++i)
67 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
68 (bset->dim->n_out-first-n)+bset->extra);
70 for (i = 0; i < bset->n_ineq; ++i)
71 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
72 (bset->dim->n_out-first-n)+bset->extra);
74 for (i = 0; i < bset->n_div; ++i)
75 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
76 (bset->dim->n_out-first-n)+bset->extra);
78 bset->dim = isl_space_drop_outputs(bset->dim, first, n);
82 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
83 bset = isl_basic_set_simplify(bset);
84 return isl_basic_set_finalize(bset);
86 isl_basic_set_free(bset);
90 struct isl_set *isl_set_drop_dims(
91 struct isl_set *set, unsigned first, unsigned n)
98 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
100 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
102 set = isl_set_cow(set);
105 set->dim = isl_space_drop_outputs(set->dim, first, n);
109 for (i = 0; i < set->n; ++i) {
110 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
115 ISL_F_CLR(set, ISL_SET_NORMALIZED);
122 /* Move "n" divs starting at "first" to the end of the list of divs.
124 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
125 unsigned first, unsigned n)
130 if (first + n == bmap->n_div)
133 div = isl_alloc_array(bmap->ctx, isl_int *, n);
136 for (i = 0; i < n; ++i)
137 div[i] = bmap->div[first + i];
138 for (i = 0; i < bmap->n_div - first - n; ++i)
139 bmap->div[first + i] = bmap->div[first + n + i];
140 for (i = 0; i < n; ++i)
141 bmap->div[bmap->n_div - n + i] = div[i];
145 isl_basic_map_free(bmap);
149 /* Drop "n" dimensions of type "type" starting at "first".
151 * In principle, this frees up some extra variables as the number
152 * of columns remains constant, but we would have to extend
153 * the div array too as the number of rows in this array is assumed
154 * to be equal to extra.
156 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
157 enum isl_dim_type type, unsigned first, unsigned n)
167 dim = isl_basic_map_dim(bmap, type);
168 isl_assert(bmap->ctx, first + n <= dim, goto error);
170 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
173 bmap = isl_basic_map_cow(bmap);
177 offset = isl_basic_map_offset(bmap, type) + first;
178 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
179 for (i = 0; i < bmap->n_eq; ++i)
180 constraint_drop_vars(bmap->eq[i]+offset, n, left);
182 for (i = 0; i < bmap->n_ineq; ++i)
183 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
185 for (i = 0; i < bmap->n_div; ++i)
186 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
188 if (type == isl_dim_div) {
189 bmap = move_divs_last(bmap, first, n);
192 isl_basic_map_free_div(bmap, n);
194 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
198 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
199 bmap = isl_basic_map_simplify(bmap);
200 return isl_basic_map_finalize(bmap);
202 isl_basic_map_free(bmap);
206 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
207 enum isl_dim_type type, unsigned first, unsigned n)
209 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
213 struct isl_basic_map *isl_basic_map_drop_inputs(
214 struct isl_basic_map *bmap, unsigned first, unsigned n)
216 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
219 struct isl_map *isl_map_drop(struct isl_map *map,
220 enum isl_dim_type type, unsigned first, unsigned n)
227 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
229 if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
231 map = isl_map_cow(map);
234 map->dim = isl_space_drop_dims(map->dim, type, first, n);
238 for (i = 0; i < map->n; ++i) {
239 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
243 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
251 struct isl_set *isl_set_drop(struct isl_set *set,
252 enum isl_dim_type type, unsigned first, unsigned n)
254 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
257 struct isl_map *isl_map_drop_inputs(
258 struct isl_map *map, unsigned first, unsigned n)
260 return isl_map_drop(map, isl_dim_in, first, n);
264 * We don't cow, as the div is assumed to be redundant.
266 static struct isl_basic_map *isl_basic_map_drop_div(
267 struct isl_basic_map *bmap, unsigned div)
275 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
277 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
279 for (i = 0; i < bmap->n_eq; ++i)
280 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
282 for (i = 0; i < bmap->n_ineq; ++i) {
283 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
284 isl_basic_map_drop_inequality(bmap, i);
288 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
291 for (i = 0; i < bmap->n_div; ++i)
292 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
294 if (div != bmap->n_div - 1) {
296 isl_int *t = bmap->div[div];
298 for (j = div; j < bmap->n_div - 1; ++j)
299 bmap->div[j] = bmap->div[j+1];
301 bmap->div[bmap->n_div - 1] = t;
303 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
304 isl_basic_map_free_div(bmap, 1);
308 isl_basic_map_free(bmap);
312 struct isl_basic_map *isl_basic_map_normalize_constraints(
313 struct isl_basic_map *bmap)
317 unsigned total = isl_basic_map_total_dim(bmap);
323 for (i = bmap->n_eq - 1; i >= 0; --i) {
324 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
325 if (isl_int_is_zero(gcd)) {
326 if (!isl_int_is_zero(bmap->eq[i][0])) {
327 bmap = isl_basic_map_set_to_empty(bmap);
330 isl_basic_map_drop_equality(bmap, i);
333 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
334 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
335 if (isl_int_is_one(gcd))
337 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
338 bmap = isl_basic_map_set_to_empty(bmap);
341 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
344 for (i = bmap->n_ineq - 1; i >= 0; --i) {
345 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
346 if (isl_int_is_zero(gcd)) {
347 if (isl_int_is_neg(bmap->ineq[i][0])) {
348 bmap = isl_basic_map_set_to_empty(bmap);
351 isl_basic_map_drop_inequality(bmap, i);
354 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
355 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
356 if (isl_int_is_one(gcd))
358 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
359 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
366 struct isl_basic_set *isl_basic_set_normalize_constraints(
367 struct isl_basic_set *bset)
369 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
370 (struct isl_basic_map *)bset);
373 /* Assumes divs have been ordered if keep_divs is set.
375 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
376 unsigned pos, isl_int *eq, int keep_divs, int *progress)
379 unsigned space_total;
383 total = isl_basic_map_total_dim(bmap);
384 space_total = isl_space_dim(bmap->dim, isl_dim_all);
385 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
386 for (k = 0; k < bmap->n_eq; ++k) {
387 if (bmap->eq[k] == eq)
389 if (isl_int_is_zero(bmap->eq[k][1+pos]))
393 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
394 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
397 for (k = 0; k < bmap->n_ineq; ++k) {
398 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
402 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
403 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
404 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
407 for (k = 0; k < bmap->n_div; ++k) {
408 if (isl_int_is_zero(bmap->div[k][0]))
410 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
414 /* We need to be careful about circular definitions,
415 * so for now we just remove the definition of div k
416 * if the equality contains any divs.
417 * If keep_divs is set, then the divs have been ordered
418 * and we can keep the definition as long as the result
421 if (last_div == -1 || (keep_divs && last_div < k))
422 isl_seq_elim(bmap->div[k]+1, eq,
423 1+pos, 1+total, &bmap->div[k][0]);
425 isl_seq_clr(bmap->div[k], 1 + total);
426 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
430 /* Assumes divs have been ordered if keep_divs is set.
432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
433 unsigned div, int keep_divs)
435 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
437 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
439 isl_basic_map_drop_div(bmap, div);
442 /* Check if elimination of div "div" using equality "eq" would not
443 * result in a div depending on a later div.
445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
450 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
451 unsigned pos = space_total + div;
453 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
454 if (last_div < 0 || last_div <= div)
457 for (k = 0; k <= last_div; ++k) {
458 if (isl_int_is_zero(bmap->div[k][0]))
460 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
467 /* Elimininate divs based on equalities
469 static struct isl_basic_map *eliminate_divs_eq(
470 struct isl_basic_map *bmap, int *progress)
477 bmap = isl_basic_map_order_divs(bmap);
482 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
484 for (d = bmap->n_div - 1; d >= 0 ; --d) {
485 for (i = 0; i < bmap->n_eq; ++i) {
486 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
487 !isl_int_is_negone(bmap->eq[i][off + d]))
489 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
493 eliminate_div(bmap, bmap->eq[i], d, 1);
494 isl_basic_map_drop_equality(bmap, i);
499 return eliminate_divs_eq(bmap, progress);
503 /* Elimininate divs based on inequalities
505 static struct isl_basic_map *eliminate_divs_ineq(
506 struct isl_basic_map *bmap, int *progress)
517 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
519 for (d = bmap->n_div - 1; d >= 0 ; --d) {
520 for (i = 0; i < bmap->n_eq; ++i)
521 if (!isl_int_is_zero(bmap->eq[i][off + d]))
525 for (i = 0; i < bmap->n_ineq; ++i)
526 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
528 if (i < bmap->n_ineq)
531 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
532 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
534 bmap = isl_basic_map_drop_div(bmap, d);
541 struct isl_basic_map *isl_basic_map_gauss(
542 struct isl_basic_map *bmap, int *progress)
550 bmap = isl_basic_map_order_divs(bmap);
555 total = isl_basic_map_total_dim(bmap);
556 total_var = total - bmap->n_div;
558 last_var = total - 1;
559 for (done = 0; done < bmap->n_eq; ++done) {
560 for (; last_var >= 0; --last_var) {
561 for (k = done; k < bmap->n_eq; ++k)
562 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
570 swap_equality(bmap, k, done);
571 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
572 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
574 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
577 if (last_var >= total_var &&
578 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
579 unsigned div = last_var - total_var;
580 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
581 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
582 isl_int_set(bmap->div[div][0],
583 bmap->eq[done][1+last_var]);
584 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
587 if (done == bmap->n_eq)
589 for (k = done; k < bmap->n_eq; ++k) {
590 if (isl_int_is_zero(bmap->eq[k][0]))
592 return isl_basic_map_set_to_empty(bmap);
594 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
598 struct isl_basic_set *isl_basic_set_gauss(
599 struct isl_basic_set *bset, int *progress)
601 return (struct isl_basic_set*)isl_basic_map_gauss(
602 (struct isl_basic_map *)bset, progress);
606 static unsigned int round_up(unsigned int v)
617 static int hash_index(isl_int ***index, unsigned int size, int bits,
618 struct isl_basic_map *bmap, int k)
621 unsigned total = isl_basic_map_total_dim(bmap);
622 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
623 for (h = hash; index[h]; h = (h+1) % size)
624 if (&bmap->ineq[k] != index[h] &&
625 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
631 struct isl_basic_set *bset, int k)
633 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
636 /* If we can eliminate more than one div, then we need to make
637 * sure we do it from last div to first div, in order not to
638 * change the position of the other divs that still need to
641 static struct isl_basic_map *remove_duplicate_divs(
642 struct isl_basic_map *bmap, int *progress)
654 if (!bmap || bmap->n_div <= 1)
657 total_var = isl_space_dim(bmap->dim, isl_dim_all);
658 total = total_var + bmap->n_div;
661 for (k = bmap->n_div - 1; k >= 0; --k)
662 if (!isl_int_is_zero(bmap->div[k][0]))
667 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
668 size = round_up(4 * bmap->n_div / 3 - 1);
669 bits = ffs(size) - 1;
670 index = isl_calloc_array(ctx, int, size);
673 eq = isl_blk_alloc(ctx, 1+total);
674 if (isl_blk_is_error(eq))
677 isl_seq_clr(eq.data, 1+total);
678 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
679 for (--k; k >= 0; --k) {
682 if (isl_int_is_zero(bmap->div[k][0]))
685 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
686 for (h = hash; index[h]; h = (h+1) % size)
687 if (isl_seq_eq(bmap->div[k],
688 bmap->div[index[h]-1], 2+total))
697 for (l = bmap->n_div - 1; l >= 0; --l) {
701 isl_int_set_si(eq.data[1+total_var+k], -1);
702 isl_int_set_si(eq.data[1+total_var+l], 1);
703 eliminate_div(bmap, eq.data, l, 0);
704 isl_int_set_si(eq.data[1+total_var+k], 0);
705 isl_int_set_si(eq.data[1+total_var+l], 0);
708 isl_blk_free(ctx, eq);
715 static int n_pure_div_eq(struct isl_basic_map *bmap)
720 total = isl_space_dim(bmap->dim, isl_dim_all);
721 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
722 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
726 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
732 /* Normalize divs that appear in equalities.
734 * In particular, we assume that bmap contains some equalities
739 * and we want to replace the set of e_i by a minimal set and
740 * such that the new e_i have a canonical representation in terms
742 * If any of the equalities involves more than one divs, then
743 * we currently simply bail out.
745 * Let us first additionally assume that all equalities involve
746 * a div. The equalities then express modulo constraints on the
747 * remaining variables and we can use "parameter compression"
748 * to find a minimal set of constraints. The result is a transformation
750 * x = T(x') = x_0 + G x'
752 * with G a lower-triangular matrix with all elements below the diagonal
753 * non-negative and smaller than the diagonal element on the same row.
754 * We first normalize x_0 by making the same property hold in the affine
756 * The rows i of G with a 1 on the diagonal do not impose any modulo
757 * constraint and simply express x_i = x'_i.
758 * For each of the remaining rows i, we introduce a div and a corresponding
759 * equality. In particular
761 * g_ii e_j = x_i - g_i(x')
763 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
764 * corresponding div (if g_kk != 1).
766 * If there are any equalities not involving any div, then we
767 * first apply a variable compression on the variables x:
769 * x = C x'' x'' = C_2 x
771 * and perform the above parameter compression on A C instead of on A.
772 * The resulting compression is then of the form
774 * x'' = T(x') = x_0 + G x'
776 * and in constructing the new divs and the corresponding equalities,
777 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
778 * by the corresponding row from C_2.
780 static struct isl_basic_map *normalize_divs(
781 struct isl_basic_map *bmap, int *progress)
788 struct isl_mat *T = NULL;
789 struct isl_mat *C = NULL;
790 struct isl_mat *C2 = NULL;
798 if (bmap->n_div == 0)
804 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
807 total = isl_space_dim(bmap->dim, isl_dim_all);
808 div_eq = n_pure_div_eq(bmap);
812 if (div_eq < bmap->n_eq) {
813 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
814 bmap->n_eq - div_eq, 0, 1 + total);
815 C = isl_mat_variable_compression(B, &C2);
819 bmap = isl_basic_map_set_to_empty(bmap);
826 d = isl_vec_alloc(bmap->ctx, div_eq);
829 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
832 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
834 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
837 B = isl_mat_product(B, C);
841 T = isl_mat_parameter_compression(B, d);
845 bmap = isl_basic_map_set_to_empty(bmap);
851 for (i = 0; i < T->n_row - 1; ++i) {
852 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
853 if (isl_int_is_zero(v))
855 isl_mat_col_submul(T, 0, v, 1 + i);
858 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
861 /* We have to be careful because dropping equalities may reorder them */
863 for (j = bmap->n_div - 1; j >= 0; --j) {
864 for (i = 0; i < bmap->n_eq; ++i)
865 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
867 if (i < bmap->n_eq) {
868 bmap = isl_basic_map_drop_div(bmap, j);
869 isl_basic_map_drop_equality(bmap, i);
875 for (i = 1; i < T->n_row; ++i) {
876 if (isl_int_is_one(T->row[i][i]))
881 if (needed > dropped) {
882 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
887 for (i = 1; i < T->n_row; ++i) {
888 if (isl_int_is_one(T->row[i][i]))
890 k = isl_basic_map_alloc_div(bmap);
891 pos[i] = 1 + total + k;
892 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
893 isl_int_set(bmap->div[k][0], T->row[i][i]);
895 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
897 isl_int_set_si(bmap->div[k][1 + i], 1);
898 for (j = 0; j < i; ++j) {
899 if (isl_int_is_zero(T->row[i][j]))
901 if (pos[j] < T->n_row && C2)
902 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
903 C2->row[pos[j]], 1 + total);
905 isl_int_neg(bmap->div[k][1 + pos[j]],
908 j = isl_basic_map_alloc_equality(bmap);
909 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
910 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
919 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
929 static struct isl_basic_map *set_div_from_lower_bound(
930 struct isl_basic_map *bmap, int div, int ineq)
932 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
934 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
935 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
936 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
937 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 isl_int_set_si(bmap->div[div][1 + total + div], 0);
943 /* Check whether it is ok to define a div based on an inequality.
944 * To avoid the introduction of circular definitions of divs, we
945 * do not allow such a definition if the resulting expression would refer to
946 * any other undefined divs or if any known div is defined in
947 * terms of the unknown div.
949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
953 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
955 /* Not defined in terms of unknown divs */
956 for (j = 0; j < bmap->n_div; ++j) {
959 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
961 if (isl_int_is_zero(bmap->div[j][0]))
965 /* No other div defined in terms of this one => avoid loops */
966 for (j = 0; j < bmap->n_div; ++j) {
969 if (isl_int_is_zero(bmap->div[j][0]))
971 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
978 /* Given two constraints "k" and "l" that are opposite to each other,
979 * except for the constant term, check if we can use them
980 * to obtain an expression for one of the hitherto unknown divs.
981 * "sum" is the sum of the constant terms of the constraints.
982 * If this sum is strictly smaller than the coefficient of one
983 * of the divs, then this pair can be used define the div.
984 * To avoid the introduction of circular definitions of divs, we
985 * do not use the pair if the resulting expression would refer to
986 * any other undefined divs or if any known div is defined in
987 * terms of the unknown div.
989 static struct isl_basic_map *check_for_div_constraints(
990 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
993 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
995 for (i = 0; i < bmap->n_div; ++i) {
996 if (!isl_int_is_zero(bmap->div[i][0]))
998 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1000 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1002 if (!ok_to_set_div_from_bound(bmap, i, k))
1004 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005 bmap = set_div_from_lower_bound(bmap, i, k);
1007 bmap = set_div_from_lower_bound(bmap, i, l);
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016 struct isl_basic_map *bmap, int *progress, int detect_divs)
1022 unsigned total = isl_basic_map_total_dim(bmap);
1026 if (!bmap || bmap->n_ineq <= 1)
1029 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1030 bits = ffs(size) - 1;
1031 ctx = isl_basic_map_get_ctx(bmap);
1032 index = isl_calloc_array(ctx, isl_int **, size);
1036 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037 for (k = 1; k < bmap->n_ineq; ++k) {
1038 h = hash_index(index, size, bits, bmap, k);
1040 index[h] = &bmap->ineq[k];
1045 l = index[h] - &bmap->ineq[0];
1046 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047 swap_inequality(bmap, k, l);
1048 isl_basic_map_drop_inequality(bmap, k);
1052 for (k = 0; k < bmap->n_ineq-1; ++k) {
1053 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054 h = hash_index(index, size, bits, bmap, k);
1055 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1058 l = index[h] - &bmap->ineq[0];
1059 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060 if (isl_int_is_pos(sum)) {
1062 bmap = check_for_div_constraints(bmap, k, l,
1066 if (isl_int_is_zero(sum)) {
1067 /* We need to break out of the loop after these
1068 * changes since the contents of the hash
1069 * will no longer be valid.
1070 * Plus, we probably we want to regauss first.
1074 isl_basic_map_drop_inequality(bmap, l);
1075 isl_basic_map_inequality_to_equality(bmap, k);
1077 bmap = isl_basic_map_set_to_empty(bmap);
1087 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1094 bmap = isl_basic_map_normalize_constraints(bmap);
1095 bmap = remove_duplicate_divs(bmap, &progress);
1096 bmap = eliminate_divs_eq(bmap, &progress);
1097 bmap = eliminate_divs_ineq(bmap, &progress);
1098 bmap = isl_basic_map_gauss(bmap, &progress);
1099 /* requires equalities in normal form */
1100 bmap = normalize_divs(bmap, &progress);
1101 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1106 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1108 return (struct isl_basic_set *)
1109 isl_basic_map_simplify((struct isl_basic_map *)bset);
1113 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1114 isl_int *constraint, unsigned div)
1121 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1123 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1125 isl_int_sub(bmap->div[div][1],
1126 bmap->div[div][1], bmap->div[div][0]);
1127 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1128 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1129 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1130 isl_int_add(bmap->div[div][1],
1131 bmap->div[div][1], bmap->div[div][0]);
1134 if (isl_seq_first_non_zero(constraint+pos+1,
1135 bmap->n_div-div-1) != -1)
1137 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1138 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1140 if (isl_seq_first_non_zero(constraint+pos+1,
1141 bmap->n_div-div-1) != -1)
1150 /* If the only constraints a div d=floor(f/m)
1151 * appears in are its two defining constraints
1154 * -(f - (m - 1)) + m d >= 0
1156 * then it can safely be removed.
1158 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1161 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1163 for (i = 0; i < bmap->n_eq; ++i)
1164 if (!isl_int_is_zero(bmap->eq[i][pos]))
1167 for (i = 0; i < bmap->n_ineq; ++i) {
1168 if (isl_int_is_zero(bmap->ineq[i][pos]))
1170 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1174 for (i = 0; i < bmap->n_div; ++i)
1175 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1182 * Remove divs that don't occur in any of the constraints or other divs.
1183 * These can arise when dropping some of the variables in a quast
1184 * returned by piplib.
1186 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1193 for (i = bmap->n_div-1; i >= 0; --i) {
1194 if (!div_is_redundant(bmap, i))
1196 bmap = isl_basic_map_drop_div(bmap, i);
1201 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1203 bmap = remove_redundant_divs(bmap);
1206 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1210 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1212 return (struct isl_basic_set *)
1213 isl_basic_map_finalize((struct isl_basic_map *)bset);
1216 struct isl_set *isl_set_finalize(struct isl_set *set)
1222 for (i = 0; i < set->n; ++i) {
1223 set->p[i] = isl_basic_set_finalize(set->p[i]);
1233 struct isl_map *isl_map_finalize(struct isl_map *map)
1239 for (i = 0; i < map->n; ++i) {
1240 map->p[i] = isl_basic_map_finalize(map->p[i]);
1244 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1252 /* Remove definition of any div that is defined in terms of the given variable.
1253 * The div itself is not removed. Functions such as
1254 * eliminate_divs_ineq depend on the other divs remaining in place.
1256 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1261 for (i = 0; i < bmap->n_div; ++i) {
1262 if (isl_int_is_zero(bmap->div[i][0]))
1264 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1266 isl_int_set_si(bmap->div[i][0], 0);
1271 /* Eliminate the specified variables from the constraints using
1272 * Fourier-Motzkin. The variables themselves are not removed.
1274 struct isl_basic_map *isl_basic_map_eliminate_vars(
1275 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1286 total = isl_basic_map_total_dim(bmap);
1288 bmap = isl_basic_map_cow(bmap);
1289 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1290 bmap = remove_dependent_vars(bmap, d);
1292 for (d = pos + n - 1;
1293 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1294 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1295 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1296 int n_lower, n_upper;
1299 for (i = 0; i < bmap->n_eq; ++i) {
1300 if (isl_int_is_zero(bmap->eq[i][1+d]))
1302 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1303 isl_basic_map_drop_equality(bmap, i);
1311 for (i = 0; i < bmap->n_ineq; ++i) {
1312 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1314 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1317 bmap = isl_basic_map_extend_constraints(bmap,
1318 0, n_lower * n_upper);
1321 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1323 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1326 for (j = 0; j < i; ++j) {
1327 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1330 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1331 isl_int_sgn(bmap->ineq[j][1+d]))
1333 k = isl_basic_map_alloc_inequality(bmap);
1336 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1338 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1339 1+d, 1+total, NULL);
1341 isl_basic_map_drop_inequality(bmap, i);
1344 if (n_lower > 0 && n_upper > 0) {
1345 bmap = isl_basic_map_normalize_constraints(bmap);
1346 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1347 bmap = isl_basic_map_gauss(bmap, NULL);
1348 bmap = isl_basic_map_remove_redundancies(bmap);
1352 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1356 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1358 bmap = isl_basic_map_gauss(bmap, NULL);
1361 isl_basic_map_free(bmap);
1365 struct isl_basic_set *isl_basic_set_eliminate_vars(
1366 struct isl_basic_set *bset, unsigned pos, unsigned n)
1368 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1369 (struct isl_basic_map *)bset, pos, n);
1372 /* Don't assume equalities are in order, because align_divs
1373 * may have changed the order of the divs.
1375 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1380 total = isl_space_dim(bmap->dim, isl_dim_all);
1381 for (d = 0; d < total; ++d)
1383 for (i = 0; i < bmap->n_eq; ++i) {
1384 for (d = total - 1; d >= 0; --d) {
1385 if (isl_int_is_zero(bmap->eq[i][1+d]))
1393 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1395 compute_elimination_index((struct isl_basic_map *)bset, elim);
1398 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1399 struct isl_basic_map *bmap, int *elim)
1405 total = isl_space_dim(bmap->dim, isl_dim_all);
1406 for (d = total - 1; d >= 0; --d) {
1407 if (isl_int_is_zero(src[1+d]))
1412 isl_seq_cpy(dst, src, 1 + total);
1415 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1420 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1421 struct isl_basic_set *bset, int *elim)
1423 return reduced_using_equalities(dst, src,
1424 (struct isl_basic_map *)bset, elim);
1427 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1428 struct isl_basic_set *bset, struct isl_basic_set *context)
1433 if (!bset || !context)
1436 if (context->n_eq == 0) {
1437 isl_basic_set_free(context);
1441 bset = isl_basic_set_cow(bset);
1445 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1448 set_compute_elimination_index(context, elim);
1449 for (i = 0; i < bset->n_eq; ++i)
1450 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1452 for (i = 0; i < bset->n_ineq; ++i)
1453 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1455 isl_basic_set_free(context);
1457 bset = isl_basic_set_simplify(bset);
1458 bset = isl_basic_set_finalize(bset);
1461 isl_basic_set_free(bset);
1462 isl_basic_set_free(context);
1466 static struct isl_basic_set *remove_shifted_constraints(
1467 struct isl_basic_set *bset, struct isl_basic_set *context)
1478 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1479 bits = ffs(size) - 1;
1480 ctx = isl_basic_set_get_ctx(bset);
1481 index = isl_calloc_array(ctx, isl_int **, size);
1485 for (k = 0; k < context->n_ineq; ++k) {
1486 h = set_hash_index(index, size, bits, context, k);
1487 index[h] = &context->ineq[k];
1489 for (k = 0; k < bset->n_ineq; ++k) {
1490 h = set_hash_index(index, size, bits, bset, k);
1493 l = index[h] - &context->ineq[0];
1494 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1496 bset = isl_basic_set_cow(bset);
1499 isl_basic_set_drop_inequality(bset, k);
1509 /* Remove all information from bset that is redundant in the context
1510 * of context. Both bset and context are assumed to be full-dimensional.
1512 * We first * remove the inequalities from "bset"
1513 * that are obviously redundant with respect to some inequality in "context".
1515 * If there are any inequalities left, we construct a tableau for
1516 * the context and then add the inequalities of "bset".
1517 * Before adding these inequalities, we freeze all constraints such that
1518 * they won't be considered redundant in terms of the constraints of "bset".
1519 * Then we detect all redundant constraints (among the
1520 * constraints that weren't frozen), first by checking for redundancy in the
1521 * the tableau and then by checking if replacing a constraint by its negation
1522 * would lead to an empty set. This last step is fairly expensive
1523 * and could be optimized by more reuse of the tableau.
1524 * Finally, we update bset according to the results.
1526 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1527 __isl_take isl_basic_set *context)
1530 isl_basic_set *combined = NULL;
1531 struct isl_tab *tab = NULL;
1532 unsigned context_ineq;
1535 if (!bset || !context)
1538 if (isl_basic_set_is_universe(bset)) {
1539 isl_basic_set_free(context);
1543 if (isl_basic_set_is_universe(context)) {
1544 isl_basic_set_free(context);
1548 bset = remove_shifted_constraints(bset, context);
1551 if (bset->n_ineq == 0)
1554 context_ineq = context->n_ineq;
1555 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1556 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1557 tab = isl_tab_from_basic_set(combined);
1558 for (i = 0; i < context_ineq; ++i)
1559 if (isl_tab_freeze_constraint(tab, i) < 0)
1561 tab = isl_tab_extend(tab, bset->n_ineq);
1562 for (i = 0; i < bset->n_ineq; ++i)
1563 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1565 bset = isl_basic_set_add_constraints(combined, bset, 0);
1569 if (isl_tab_detect_redundant(tab) < 0)
1571 total = isl_basic_set_total_dim(bset);
1572 for (i = context_ineq; i < bset->n_ineq; ++i) {
1574 if (tab->con[i].is_redundant)
1576 tab->con[i].is_redundant = 1;
1577 combined = isl_basic_set_dup(bset);
1578 combined = isl_basic_set_update_from_tab(combined, tab);
1579 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1580 k = isl_basic_set_alloc_inequality(combined);
1583 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1584 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1585 is_empty = isl_basic_set_is_empty(combined);
1588 isl_basic_set_free(combined);
1591 tab->con[i].is_redundant = 0;
1593 for (i = 0; i < context_ineq; ++i)
1594 tab->con[i].is_redundant = 1;
1595 bset = isl_basic_set_update_from_tab(bset, tab);
1597 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1598 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1603 bset = isl_basic_set_simplify(bset);
1604 bset = isl_basic_set_finalize(bset);
1605 isl_basic_set_free(context);
1609 isl_basic_set_free(combined);
1610 isl_basic_set_free(context);
1611 isl_basic_set_free(bset);
1615 /* Remove all information from bset that is redundant in the context
1616 * of context. In particular, equalities that are linear combinations
1617 * of those in context are removed. Then the inequalities that are
1618 * redundant in the context of the equalities and inequalities of
1619 * context are removed.
1621 * We first compute the integer affine hull of the intersection,
1622 * compute the gist inside this affine hull and then add back
1623 * those equalities that are not implied by the context.
1625 * If two constraints are mutually redundant, then uset_gist_full
1626 * will remove the second of those constraints. We therefore first
1627 * sort the constraints so that constraints not involving existentially
1628 * quantified variables are given precedence over those that do.
1629 * We have to perform this sorting before the variable compression,
1630 * because that may effect the order of the variables.
1632 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1633 __isl_take isl_basic_set *context)
1638 isl_basic_set *aff_context;
1641 if (!bset || !context)
1644 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1645 if (isl_basic_set_plain_is_empty(bset)) {
1646 isl_basic_set_free(context);
1649 bset = isl_basic_set_sort_constraints(bset);
1650 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1653 if (isl_basic_set_plain_is_empty(aff)) {
1654 isl_basic_set_free(aff);
1655 isl_basic_set_free(context);
1658 if (aff->n_eq == 0) {
1659 isl_basic_set_free(aff);
1660 return uset_gist_full(bset, context);
1662 total = isl_basic_set_total_dim(bset);
1663 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1664 eq = isl_mat_cow(eq);
1665 T = isl_mat_variable_compression(eq, &T2);
1666 if (T && T->n_col == 0) {
1669 isl_basic_set_free(context);
1670 isl_basic_set_free(aff);
1671 return isl_basic_set_set_to_empty(bset);
1674 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1676 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1677 context = isl_basic_set_preimage(context, T);
1679 bset = uset_gist_full(bset, context);
1680 bset = isl_basic_set_preimage(bset, T2);
1681 bset = isl_basic_set_intersect(bset, aff);
1682 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1685 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1686 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1691 isl_basic_set_free(bset);
1692 isl_basic_set_free(context);
1696 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1697 * We simply add the equalities in context to bmap and then do a regular
1698 * div normalizations. Better results can be obtained by normalizing
1699 * only the divs in bmap than do not also appear in context.
1700 * We need to be careful to reduce the divs using the equalities
1701 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1702 * spurious constraints.
1704 static struct isl_basic_map *normalize_divs_in_context(
1705 struct isl_basic_map *bmap, struct isl_basic_map *context)
1708 unsigned total_context;
1711 div_eq = n_pure_div_eq(bmap);
1715 if (context->n_div > 0)
1716 bmap = isl_basic_map_align_divs(bmap, context);
1718 total_context = isl_basic_map_total_dim(context);
1719 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1720 for (i = 0; i < context->n_eq; ++i) {
1722 k = isl_basic_map_alloc_equality(bmap);
1723 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1724 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1725 isl_basic_map_total_dim(bmap) - total_context);
1727 bmap = isl_basic_map_gauss(bmap, NULL);
1728 bmap = normalize_divs(bmap, NULL);
1729 bmap = isl_basic_map_gauss(bmap, NULL);
1733 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1734 struct isl_basic_map *context)
1736 struct isl_basic_set *bset;
1738 if (!bmap || !context)
1741 if (isl_basic_map_is_universe(bmap)) {
1742 isl_basic_map_free(context);
1745 if (isl_basic_map_plain_is_empty(context)) {
1746 isl_space *dim = isl_space_copy(bmap->dim);
1747 isl_basic_map_free(context);
1748 isl_basic_map_free(bmap);
1749 return isl_basic_map_universe(dim);
1751 if (isl_basic_map_plain_is_empty(bmap)) {
1752 isl_basic_map_free(context);
1756 bmap = isl_basic_map_remove_redundancies(bmap);
1757 context = isl_basic_map_remove_redundancies(context);
1760 bmap = normalize_divs_in_context(bmap, context);
1762 context = isl_basic_map_align_divs(context, bmap);
1763 bmap = isl_basic_map_align_divs(bmap, context);
1765 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1766 isl_basic_map_underlying_set(context));
1768 return isl_basic_map_overlying_set(bset, bmap);
1770 isl_basic_map_free(bmap);
1771 isl_basic_map_free(context);
1776 * Assumes context has no implicit divs.
1778 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1779 __isl_take isl_basic_map *context)
1783 if (!map || !context)
1786 if (isl_basic_map_plain_is_empty(context)) {
1787 isl_space *dim = isl_space_copy(map->dim);
1788 isl_basic_map_free(context);
1790 return isl_map_universe(dim);
1793 context = isl_basic_map_remove_redundancies(context);
1794 map = isl_map_cow(map);
1795 if (!map || !context)
1797 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1798 map = isl_map_compute_divs(map);
1799 for (i = 0; i < map->n; ++i)
1800 context = isl_basic_map_align_divs(context, map->p[i]);
1801 for (i = map->n - 1; i >= 0; --i) {
1802 map->p[i] = isl_basic_map_gist(map->p[i],
1803 isl_basic_map_copy(context));
1806 if (isl_basic_map_plain_is_empty(map->p[i])) {
1807 isl_basic_map_free(map->p[i]);
1808 if (i != map->n - 1)
1809 map->p[i] = map->p[map->n - 1];
1813 isl_basic_map_free(context);
1814 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1818 isl_basic_map_free(context);
1822 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1823 __isl_take isl_map *context)
1825 context = isl_map_compute_divs(context);
1826 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1829 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1830 __isl_take isl_map *context)
1832 return isl_map_align_params_map_map_and(map, context, &map_gist);
1835 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1836 struct isl_basic_set *context)
1838 return (struct isl_basic_set *)isl_basic_map_gist(
1839 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1842 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1843 __isl_take isl_basic_set *context)
1845 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1846 (struct isl_basic_map *)context);
1849 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1850 __isl_take isl_set *context)
1852 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1853 (struct isl_map *)context);
1856 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1857 __isl_take isl_set *context)
1859 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1860 map_context = isl_map_intersect_params(map_context, context);
1861 return isl_map_gist(map, map_context);
1864 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1865 __isl_take isl_set *context)
1867 return isl_map_gist_params(set, context);
1870 /* Quick check to see if two basic maps are disjoint.
1871 * In particular, we reduce the equalities and inequalities of
1872 * one basic map in the context of the equalities of the other
1873 * basic map and check if we get a contradiction.
1875 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1876 __isl_keep isl_basic_map *bmap2)
1878 struct isl_vec *v = NULL;
1883 if (!bmap1 || !bmap2)
1885 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1887 if (bmap1->n_div || bmap2->n_div)
1889 if (!bmap1->n_eq && !bmap2->n_eq)
1892 total = isl_space_dim(bmap1->dim, isl_dim_all);
1895 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1898 elim = isl_alloc_array(bmap1->ctx, int, total);
1901 compute_elimination_index(bmap1, elim);
1902 for (i = 0; i < bmap2->n_eq; ++i) {
1904 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1906 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1907 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1910 for (i = 0; i < bmap2->n_ineq; ++i) {
1912 reduced = reduced_using_equalities(v->block.data,
1913 bmap2->ineq[i], bmap1, elim);
1914 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1915 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1918 compute_elimination_index(bmap2, elim);
1919 for (i = 0; i < bmap1->n_ineq; ++i) {
1921 reduced = reduced_using_equalities(v->block.data,
1922 bmap1->ineq[i], bmap2, elim);
1923 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1924 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1940 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1941 __isl_keep isl_basic_set *bset2)
1943 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1944 (struct isl_basic_map *)bset2);
1947 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1948 __isl_keep isl_map *map2)
1955 if (isl_map_plain_is_equal(map1, map2))
1958 for (i = 0; i < map1->n; ++i) {
1959 for (j = 0; j < map2->n; ++j) {
1960 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1969 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1970 __isl_keep isl_set *set2)
1972 return isl_map_plain_is_disjoint((struct isl_map *)set1,
1973 (struct isl_map *)set2);
1976 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
1978 return isl_set_plain_is_disjoint(set1, set2);
1981 /* Check if we can combine a given div with lower bound l and upper
1982 * bound u with some other div and if so return that other div.
1983 * Otherwise return -1.
1985 * We first check that
1986 * - the bounds are opposites of each other (except for the constant
1988 * - the bounds do not reference any other div
1989 * - no div is defined in terms of this div
1991 * Let m be the size of the range allowed on the div by the bounds.
1992 * That is, the bounds are of the form
1994 * e <= a <= e + m - 1
1996 * with e some expression in the other variables.
1997 * We look for another div b such that no third div is defined in terms
1998 * of this second div b and such that in any constraint that contains
1999 * a (except for the given lower and upper bound), also contains b
2000 * with a coefficient that is m times that of b.
2001 * That is, all constraints (execpt for the lower and upper bound)
2004 * e + f (a + m b) >= 0
2006 * If so, we return b so that "a + m b" can be replaced by
2007 * a single div "c = a + m b".
2009 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2010 unsigned div, unsigned l, unsigned u)
2016 if (bmap->n_div <= 1)
2018 dim = isl_space_dim(bmap->dim, isl_dim_all);
2019 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2021 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2022 bmap->n_div - div - 1) != -1)
2024 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2028 for (i = 0; i < bmap->n_div; ++i) {
2029 if (isl_int_is_zero(bmap->div[i][0]))
2031 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2035 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2036 if (isl_int_is_neg(bmap->ineq[l][0])) {
2037 isl_int_sub(bmap->ineq[l][0],
2038 bmap->ineq[l][0], bmap->ineq[u][0]);
2039 bmap = isl_basic_map_copy(bmap);
2040 bmap = isl_basic_map_set_to_empty(bmap);
2041 isl_basic_map_free(bmap);
2044 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2045 for (i = 0; i < bmap->n_div; ++i) {
2050 for (j = 0; j < bmap->n_div; ++j) {
2051 if (isl_int_is_zero(bmap->div[j][0]))
2053 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2056 if (j < bmap->n_div)
2058 for (j = 0; j < bmap->n_ineq; ++j) {
2060 if (j == l || j == u)
2062 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2064 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2066 isl_int_mul(bmap->ineq[j][1 + dim + div],
2067 bmap->ineq[j][1 + dim + div],
2069 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2070 bmap->ineq[j][1 + dim + i]);
2071 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2072 bmap->ineq[j][1 + dim + div],
2077 if (j < bmap->n_ineq)
2082 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2083 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2087 /* Given a lower and an upper bound on div i, construct an inequality
2088 * that when nonnegative ensures that this pair of bounds always allows
2089 * for an integer value of the given div.
2090 * The lower bound is inequality l, while the upper bound is inequality u.
2091 * The constructed inequality is stored in ineq.
2092 * g, fl, fu are temporary scalars.
2094 * Let the upper bound be
2098 * and the lower bound
2102 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2105 * - f_u e_l <= f_u f_l g a <= f_l e_u
2107 * Since all variables are integer valued, this is equivalent to
2109 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2111 * If this interval is at least f_u f_l g, then it contains at least
2112 * one integer value for a.
2113 * That is, the test constraint is
2115 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2117 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2118 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2121 dim = isl_space_dim(bmap->dim, isl_dim_all);
2123 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2124 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2125 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2126 isl_int_neg(fu, fu);
2127 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2128 1 + dim + bmap->n_div);
2129 isl_int_add(ineq[0], ineq[0], fl);
2130 isl_int_add(ineq[0], ineq[0], fu);
2131 isl_int_sub_ui(ineq[0], ineq[0], 1);
2132 isl_int_mul(g, g, fl);
2133 isl_int_mul(g, g, fu);
2134 isl_int_sub(ineq[0], ineq[0], g);
2137 /* Remove more kinds of divs that are not strictly needed.
2138 * In particular, if all pairs of lower and upper bounds on a div
2139 * are such that they allow at least one integer value of the div,
2140 * the we can eliminate the div using Fourier-Motzkin without
2141 * introducing any spurious solutions.
2143 static struct isl_basic_map *drop_more_redundant_divs(
2144 struct isl_basic_map *bmap, int *pairs, int n)
2146 struct isl_tab *tab = NULL;
2147 struct isl_vec *vec = NULL;
2159 dim = isl_space_dim(bmap->dim, isl_dim_all);
2160 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2164 tab = isl_tab_from_basic_map(bmap);
2169 enum isl_lp_result res;
2171 for (i = 0; i < bmap->n_div; ++i) {
2174 if (best >= 0 && pairs[best] <= pairs[i])
2180 for (l = 0; l < bmap->n_ineq; ++l) {
2181 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2183 for (u = 0; u < bmap->n_ineq; ++u) {
2184 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2186 construct_test_ineq(bmap, i, l, u,
2187 vec->el, g, fl, fu);
2188 res = isl_tab_min(tab, vec->el,
2189 bmap->ctx->one, &g, NULL, 0);
2190 if (res == isl_lp_error)
2192 if (res == isl_lp_empty) {
2193 bmap = isl_basic_map_set_to_empty(bmap);
2196 if (res != isl_lp_ok || isl_int_is_neg(g))
2199 if (u < bmap->n_ineq)
2202 if (l == bmap->n_ineq) {
2222 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2223 return isl_basic_map_drop_redundant_divs(bmap);
2226 isl_basic_map_free(bmap);
2235 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2236 * and the upper bound u, div1 always occurs together with div2 in the form
2237 * (div1 + m div2), where m is the constant range on the variable div1
2238 * allowed by l and u, replace the pair div1 and div2 by a single
2239 * div that is equal to div1 + m div2.
2241 * The new div will appear in the location that contains div2.
2242 * We need to modify all constraints that contain
2243 * div2 = (div - div1) / m
2244 * (If a constraint does not contain div2, it will also not contain div1.)
2245 * If the constraint also contains div1, then we know they appear
2246 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2247 * i.e., the coefficient of div is f.
2249 * Otherwise, we first need to introduce div1 into the constraint.
2258 * A lower bound on div2
2262 * can be replaced by
2264 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2266 * with g = gcd(m,n).
2271 * can be replaced by
2273 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2275 * These constraint are those that we would obtain from eliminating
2276 * div1 using Fourier-Motzkin.
2278 * After all constraints have been modified, we drop the lower and upper
2279 * bound and then drop div1.
2281 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2282 unsigned div1, unsigned div2, unsigned l, unsigned u)
2287 unsigned dim, total;
2290 dim = isl_space_dim(bmap->dim, isl_dim_all);
2291 total = 1 + dim + bmap->n_div;
2296 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2297 isl_int_add_ui(m, m, 1);
2299 for (i = 0; i < bmap->n_ineq; ++i) {
2300 if (i == l || i == u)
2302 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2304 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2305 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2306 isl_int_divexact(a, m, b);
2307 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2308 if (isl_int_is_pos(b)) {
2309 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2310 b, bmap->ineq[l], total);
2313 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2314 b, bmap->ineq[u], total);
2317 isl_int_set(bmap->ineq[i][1 + dim + div2],
2318 bmap->ineq[i][1 + dim + div1]);
2319 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2326 isl_basic_map_drop_inequality(bmap, l);
2327 isl_basic_map_drop_inequality(bmap, u);
2329 isl_basic_map_drop_inequality(bmap, u);
2330 isl_basic_map_drop_inequality(bmap, l);
2332 bmap = isl_basic_map_drop_div(bmap, div1);
2336 /* First check if we can coalesce any pair of divs and
2337 * then continue with dropping more redundant divs.
2339 * We loop over all pairs of lower and upper bounds on a div
2340 * with coefficient 1 and -1, respectively, check if there
2341 * is any other div "c" with which we can coalesce the div
2342 * and if so, perform the coalescing.
2344 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2345 struct isl_basic_map *bmap, int *pairs, int n)
2350 dim = isl_space_dim(bmap->dim, isl_dim_all);
2352 for (i = 0; i < bmap->n_div; ++i) {
2355 for (l = 0; l < bmap->n_ineq; ++l) {
2356 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2358 for (u = 0; u < bmap->n_ineq; ++u) {
2361 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2363 c = div_find_coalesce(bmap, pairs, i, l, u);
2367 bmap = coalesce_divs(bmap, i, c, l, u);
2368 return isl_basic_map_drop_redundant_divs(bmap);
2373 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2376 return drop_more_redundant_divs(bmap, pairs, n);
2379 /* Remove divs that are not strictly needed.
2380 * In particular, if a div only occurs positively (or negatively)
2381 * in constraints, then it can simply be dropped.
2382 * Also, if a div occurs only occurs in two constraints and if moreover
2383 * those two constraints are opposite to each other, except for the constant
2384 * term and if the sum of the constant terms is such that for any value
2385 * of the other values, there is always at least one integer value of the
2386 * div, i.e., if one plus this sum is greater than or equal to
2387 * the (absolute value) of the coefficent of the div in the constraints,
2388 * then we can also simply drop the div.
2390 * If any divs are left after these simple checks then we move on
2391 * to more complicated cases in drop_more_redundant_divs.
2393 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2394 struct isl_basic_map *bmap)
2404 off = isl_space_dim(bmap->dim, isl_dim_all);
2405 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2409 for (i = 0; i < bmap->n_div; ++i) {
2411 int last_pos, last_neg;
2415 defined = !isl_int_is_zero(bmap->div[i][0]);
2416 for (j = 0; j < bmap->n_eq; ++j)
2417 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2423 for (j = 0; j < bmap->n_ineq; ++j) {
2424 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2428 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2433 pairs[i] = pos * neg;
2434 if (pairs[i] == 0) {
2435 for (j = bmap->n_ineq - 1; j >= 0; --j)
2436 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2437 isl_basic_map_drop_inequality(bmap, j);
2438 bmap = isl_basic_map_drop_div(bmap, i);
2440 return isl_basic_map_drop_redundant_divs(bmap);
2444 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2445 bmap->ineq[last_neg] + 1,
2449 isl_int_add(bmap->ineq[last_pos][0],
2450 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2451 isl_int_add_ui(bmap->ineq[last_pos][0],
2452 bmap->ineq[last_pos][0], 1);
2453 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2454 bmap->ineq[last_pos][1+off+i]);
2455 isl_int_sub_ui(bmap->ineq[last_pos][0],
2456 bmap->ineq[last_pos][0], 1);
2457 isl_int_sub(bmap->ineq[last_pos][0],
2458 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2461 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2466 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2467 bmap = isl_basic_map_simplify(bmap);
2469 return isl_basic_map_drop_redundant_divs(bmap);
2471 if (last_pos > last_neg) {
2472 isl_basic_map_drop_inequality(bmap, last_pos);
2473 isl_basic_map_drop_inequality(bmap, last_neg);
2475 isl_basic_map_drop_inequality(bmap, last_neg);
2476 isl_basic_map_drop_inequality(bmap, last_pos);
2478 bmap = isl_basic_map_drop_div(bmap, i);
2480 return isl_basic_map_drop_redundant_divs(bmap);
2484 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2490 isl_basic_map_free(bmap);
2494 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2495 struct isl_basic_set *bset)
2497 return (struct isl_basic_set *)
2498 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2501 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2507 for (i = 0; i < map->n; ++i) {
2508 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2512 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2519 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2521 return (struct isl_set *)
2522 isl_map_drop_redundant_divs((struct isl_map *)set);